We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally symmetric subspaces, we work out the constraints on torsion in two different theoretical schemes. We show that at least for a completely antisymmetric torsion tensor (for e.g. the one motivated from string theory), an equivalence is set between these two schemes, as the non-vanishing independent torsion tensor components turn out to be the same.
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.
We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the or…
We report a search for new gravitational physics phenomena based on Einstein-Cartan theory of General Relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth and Cabi, we analyze the motion of test bodies in the presence of torsion, and in particular we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general may differ from geodesics when torsion is present. We deriv…
We present an analysis of an $f(T, \mathcal{T})$ extension of the Teleparallel Equivalent of General Relativity, where $T$ denotes the torsion and $\mathcal{T}$ the trace of the energy-momentum tensor. This extension includes non--minimal couplings between torsion and matter. In particular, we construct two specific models that recover the usual continuity equation, namely, $f(T, \mathcal{T})=T+g(\mathcal{T})$ and $f(T, \mathcal{T})=T\times g(\mathcal{T})$. We then constrain the parameters of each model by fitting the predicted distance modulus to that measured from type Ia supernovae, and fin…
The paper deals with cosmological solutions describing different phases of the Universe for the homogeneous and isotropic FLRW model of the Universe with torsion. Normally, torsion field is not suitable for maximally symmetric space time model. However, one may use a specific profile of vectorial torsion field, derived from a scalar function. By proper choices of the torsion scalar function, it is shown that a continuous cosmic evolution starting from the emergent scenario to the present late time acceleration is possible. Also thermodynamics of the system is analyzed and equivalence with Eins…
We used a stationary torsion balance with a beryllium-aluminum composition dipole to search for ultra low-mass bosonic dark matter coupled to baryon minus lepton number. We set 95% confidence limits on the coupling constant $g_{\rm B-L}$ for bosons with masses between $10^{-18}$ and $10^{-16}$ eV/$c^2$ with the best performance at $m_{\rm DM} = 8\times 10^{-18}$ eV/$c^2$ constraining $g_{B-L}(\hbar c)^{-1/2} < 1 \times 10^{-25}$. This provides a complimentary limit to equivalence-principle experiments that search for ultra low-mass bosons as force-mediating particles.
Constraining Light Scalar Field with Torsion-Balance Gravity Experiments
Henan International Joint Laboratory of MXene Materials Microstructure, College of Physics and Electronic Engineering, Nanyang Normal University（南阳师范学院物理与电子工程学院）；School of Mechanical Engineering and Electronic Information, China University of Geosciences（中国地质大学机械电子工程学院）；Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences（中国科学院光电技术研究所）
Presented is a quantum gravity theory that is a quantum mechanical generalization of Einstein's vierbein field-based approach, where the classical metric tensor field is promoted to a quantum mechanical metric tensor field operator. The quantum gravity theory derives from quantum information dynamics intrinsic to quantized space, which is taken to be a tensor product space on a qubit array. Hence, the metric tensor field operator is expressed as a product of two frame 4-vectors, which are anticommuting operators and naturally represented by Dirac matrices. The quantum gravity theory reduces to…
Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity à la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of General Relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to non-metricity. The latter allows a simpler geometrical formulation of General Relativity that is oblivious …
The linearized massive gravity in three dimensions, over any maximally symmetric background, is known to be presented in a self-dual form as a first order equation which encodes not only the massive Klein-Gordon type field equation but also the supplementary transverse-traceless conditions. We generalize this construction to higher dimensions. The appropriate dual description in d dimensions, additionally to a (non-symmetric) tensor field $h_{μν}$, involves an extra rank-(d-1) field equivalently represented by the torsion rank-3 tensor. The symmetry condition for $h_{μν}$ arises on-shell as a …
